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Rep. Tim Scott's Capitol Hill fans

State law gives the Republican governor the authority to pick DeMint's successor. DeMint announced less than two weeks ago that he would resign Jan. 1 to take the helm of a national conservative think tank.

Haley's appointee will fill the seat until 2014, when voters will choose who will fill the remaining two years of DeMint's term.

Haley's five finalists are reportedly former first lady Jenny Sanford, U.S. Reps. Tim Scott and Trey Gowdy, former Attorney General Henry McMaster and state health agency director Catherine Templeton.